Multiplier theorem on generalized Heisenberg groups

Waldemar Hebisch

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 2, page 231-239
  • ISSN: 0010-1354

How to cite


Hebisch, Waldemar. "Multiplier theorem on generalized Heisenberg groups." Colloquium Mathematicae 65.2 (1993): 231-239. <>.

author = {Hebisch, Waldemar},
journal = {Colloquium Mathematicae},
keywords = { boundedness; sublaplacian; generalized Heisenberg groups; Hörmander result; Fourier multipliers},
language = {eng},
number = {2},
pages = {231-239},
title = {Multiplier theorem on generalized Heisenberg groups},
url = {},
volume = {65},
year = {1993},

AU - Hebisch, Waldemar
TI - Multiplier theorem on generalized Heisenberg groups
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 2
SP - 231
EP - 239
LA - eng
KW - boundedness; sublaplacian; generalized Heisenberg groups; Hörmander result; Fourier multipliers
UR -
ER -


  1. [1] M. Christ, L p bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81. Zbl0739.42010
  2. [2] J. Cygan, Heat kernels for class 2 nilpotent groups, Studia Math. 64 (1979), 227-238. Zbl0336.35029
  3. [3] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, 1982. Zbl0508.42025
  4. [4] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimations sous-elliptiques sur certains groupes nilpotents, Acta Math. 139 (1977), 95-153. 
  5. [5] W. Hebisch, A multiplier theorem for Schrödinger operators, Colloq. Math. 60/61 (1990), 659-664. Zbl0779.35025
  6. [6] --, Almost everywhere summability of eigenfunction expansions associated to elliptic operators, Studia Math. 96 (1990), 263-275. Zbl0716.35053
  7. [7] A. Hulanicki, Subalgebra of L 1 ( G ) associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. Zbl0316.43005
  8. [8] --, The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math. 56 (1976), 165-173. Zbl0336.22007
  9. [9] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, ibid. 80 (1984), 235-244. 
  10. [10] G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 6 (1990), 141-154. Zbl0763.43005
  11. [11] H. P. McKean, -Δ plus a bad potential, J. Math. Phys. 18 (1977), 1277-1279. 
  12. [12] D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl., to appear. Zbl0838.43011
  13. [13] J. Randall, The heat kernel for generalized Heisenberg groups, to appear. Zbl0897.43007

Citations in EuDML Documents

  1. Elias M. Stein, Spectral multipliers and multiple-parameter structures on the Heisenberg group
  2. Waldemar Hebisch, Boundedness of L 1 spectral multipliers for an exponential solvable Lie group
  3. Waldemar Hebisch, Jacek Zienkiewicz, Multiplier theorem on generalized Heisenberg groups II
  4. Sami Mustapha, Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires
  5. Alessio Martini, Analysis of joint spectral multipliers on Lie groups of polynomial growth
  6. Giancarlo Mauceri, Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck
  7. Detlef Müller, Sub-Laplacians of holomorphic L p -type on exponential Lie groups

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